Atom fraction, defined

In this section we study the competitive solvation of PVA in ethanol-water mixture. For this propose the concept of local atomic fractions, defined as follow, has been used by Mtiller-Plathe and van Gunsteren [79]... 

An estimate of AR ia alloys can be made usiug the empirical expression (12) of equation 10 where the average alloy reduced energy, is defined by equation 11, where C (i = 1, 2,... , n) is the elemental atomic fraction of the /th element, and is the elemental reduced energy defined iu equation 3. Using this formulation, the projected range straggling iu compounds can be calculated to within 20%. 

FIG. 5 Local concentration profiles around a hydroxyl group in poly(vinyl alcohol) of heavy atoms in a (1 1) water/ethanol mixture A = OW water oxygen, A = OE ethanol oxygen, A = CE ethanol carbon. The local atomic fractions are defined as = a( )/ ZIb where a( ) is average number of atoms... 

If the atom fraction of deuterium in each separated coal product, given in Table I, is defined as Fy, the atom fraction of protium in the same coal product is therefore 1-Fy. The total amount of protium and deuterium in a given product fraction y is normalized to unity according to Equation 3,... 

All binary alloy compositions listed in this chapter will be written as atomic fractions. For convenience, we will define the symbol a/o as 100% N, where N is the atomic fraction of an element in the alloy. For example, an alloy containing 20% atomic fraction aluminum will be referred to as 20 a/o Al. 

As a comment to the atomic dimensions concept, two rules , Vegard s andBiltz-Zen s rules, formulated for solid solutions, and to a certain extent for ordered compounds can be mentioned here. These rules, mutually incompatible, are very seldom obeyed they may however be useful either as approximations or for defining reference behaviours. The first one, Vegard s rule (1921), corresponds to an additivity rule for interatomic distances (or lattice parameters or average atomic diameters). For a solid solution (x = atomic fraction) between two components of... 

There is a regularly returning confusion, why the generated X-ray intensity is proportional to the mass fraction of the elements present, in contrast to the atomic fraction. This fact is contradictory to our first physical anticipation, since the ionization cross section is defined for one atom, so it is the number of atoms that should be important (irrespective of their masses). It is a correct assumption and we recall it below, how the mass fraction results from the starting number of atoms. 

Defining atom fractions of the components x, and mole fractions of species yi by a generalization of Eqs. (28) and (29), the mole fractions of the uncombined species are obtained from Eqs. (54)—(56) as... 

The intensity of an XPS peak (Ia) is a strong function of (i) the incoming photon flux, (ii) the concentration of the given element, (hi) its photoionization cross-section (which is excitation-energy dependent), (iv) the mean free path of the emitted photoelectron, and (v) further instrumental parameters (such as photoelectron collection and detection efficiency). By defining atomic sensitivity factors (S, as an overall factor summing up the effects of iii-v), the atom fraction of any element in a sample can be calculated as ... 

Segregation effects at the liquid-solid interface are controlled by the equilibrium distribution coefficient, k q, which is defined as the ratio of the solidus and the liquidus concentrations in atomic fractions ... 

The so-called Jurs descriptors are 3D surface descriptions related to various total and fractional defined surfaces. They can be divided into to two parts one electronic [35] and one hydrophobic [36]. The former set of descriptors is generated from partial positive and negative surface areas, total charge as well as atomic positively and negatively charged weighted surface areas, and various differential and fractional charged partial surface areas of the molecule (see Table 14.3). 

Some relations for isotope separation plants are simpler when expressed as weight, mole, or atom ratios, defined as the ratio of the fraction of one component to the fraction of a second. These ratios are denoted by Greek letters f,, or r) for feed, depleted, or enriched stream, corresponding to z, x, or y. In a two-component mixture, these ratios are defined as the ratio of the fraction of the desired component to that of the other component. For example, in a tails stream, the weight, mole of atom ratio for a two-component mixture is... 

The increase in deuterium content per stage is measured by the heads enrichment factor 0, defined in terms of the atom fraction deuterium in the heads water leaving this stage x and the atom fraction deuterium in the water leaving the next lower stage, as... 

If an element consists of H atoms of isotope 1, n atoms of isotope 2, etc., the atomic fraction for isotope 1 is defined as ... 

The atomic mass of an element (or atomic weight) M is defined as the average of the isotopic masses, i.e. is weighted by the atomic fraction Xf of its isotope ... 

The standard state corresponds to a solid alone in its own phase at standard pressure P°. Solids are frequently found in their standard state. However in electrochemistry there are cases where the solid phase is a solid solution, for example with metal alloys or insertion materials used in many batteries. Here therefore the activities are defined using composition parameters (for example with the atomic fraction for alloys, or the concentration for solid electrolytes, etc.). 

Several key parameters are calculated in quantifying green chanistry. As discussed in Section 14.9, one of these is atom economy, defined as the fraction of reactant material that actually ends up in the final product. The higher the atom economy—ideally 100%—the greener the process. Other important parameters include the E factor, which measures wastes (Section 14.9), and oxygen and hydrogen availability (Section 14.14). 

Mole (or atom) fraction is defined as the number of q-moles (or a-atoms) of substance divided by the total number of g-moles (or g-atoms) of all the substances comprising the solution. Thus, in a multi-component solution... 

This standard state is so defined that the Henrian activity approaches the atom fraction at infinite dilution, i.e. 

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